After much wailing and gnashing of teeth I persuaded the man of the house to remodel the kitchen. Fortunately the wailing and gnashing will henceforth come mostly from the contractor as we decided the job is beyond our amateur home-handyman skills.
Here's the final layout we picked after multiple iterations. A couple of things to note: there is water behind the wall where the new sink and dishwasher are going to be. That definitely influenced the placement. Putting them elsewhere would have involved a significant expense of digging a trench out for the plumbing in our slab floor.
The sliding doors face North, which isn't ideal but will get better light into the room than does the window which is there now. We're getting sliders with built in blinds. I've never liked curtains on doors so the built in option seems the best solution. Also keeping fabric out of the kitchen is a good way to reduce lingering smells.
The other, single entry faces South; beside it is a counter-depth fridge. In the corner is a prep sink, replacing the un-ergonomic two-basin sink that is there now (see the before pics). On the East wall is a range and microwave. On the West wall is my existing pantry closet and a new build out of dishwasher, main sink, and more counter space.
The island in the middle took some time for me to get my mind around. Initially I thought a peninsula would be better but no matter how we tried it, we ended up with significant dead space in the kitchen. An island solves dual problems of 1) more counter space and 2) a small dining area for two people while permitting full use of the space.
Thanks to Alison at Kitchen Master for the lovely design.